{"id":6470,"date":"2012-09-27T06:00:53","date_gmt":"2012-09-27T13:00:53","guid":{"rendered":"http:\/\/dabacon.org\/pontiff\/?p=6470"},"modified":"2012-09-27T06:00:53","modified_gmt":"2012-09-27T13:00:53","slug":"uncertain-on-uncertainty","status":"publish","type":"post","link":"https:\/\/dabacon.org\/pontiff\/2012\/09\/27\/uncertain-on-uncertainty\/","title":{"rendered":"Uncertain on Uncertainty"},"content":{"rendered":"

Over at BBC News, there is an\u00a0article<\/a> about a recently published\u00a0paper\u00a0(arXiv<\/a>) by Lee Rozema et al<\/em>. that could lead to some, ehm, uncertainty<\/em> about the status of the Heisenberg Uncertainty Principle (HUP).
\nBefore\u00a0dissecting\u00a0the BBC article, let’s look at the paper by Rozema et al<\/em>. The title is “Violation of Heisenberg\u2019s Measurement–Disturbance Relationship by Weak Measurements”.\u00a0While this title might raise a few eyebrows, the authors make it crystal clear in the opening sentence of the abstract that they didn’t disprove the HUP or some such nonsense. The HUP is a theorem<\/em> within the standard formulation of quantum mechanics, so finding a violation of that would be equivalent to finding a violation of quantum theory itself! Instead, they look at the so-called measurement–disturbance relationship (MDR), which is a non-rigorous heuristic that is commonly taught to give an intuition for the uncertainty principle.
\nThe HUP is usually stated in the form of the\u00a0Robertson uncertainty relation<\/a>, and states that a given quantum state $latex psi$ cannot (in general) have zero variance with respect to two non-commuting observables. The more modern formulations are stated in a why that is independent of the quantum state; see this nice review by\u00a0Wehner and Winter<\/a>\u00a0for more about these\u00a0entropic<\/em> uncertainty relations.
\nBy contrast, the MDR states\u00a0that the product of the measurement precision and the measurement disturbance (quantified as root-mean-squared deviations between ideal and actual measurement variables) can’t be smaller than Planck’s constant. In 2002,\u00a0Masanao Ozawa proved<\/a>\u00a0that this was inconsistent<\/em> with standard quantum mechanics, and formulated a corrected version<\/a>\u00a0of the MDR that also takes into account the state-dependent variance of the observables. Building on Ozawa’s work, in 2010\u00a0Lund and Wiseman<\/a>\u00a0proposed an experiment which could measure the relevant quantities using\u00a0\u00a0the so-called\u00a0weak value<\/a>.
\nRozema et al<\/em>. implemented the Lund-Wiseman scheme using measurements of complementary observables ($latex X$ and $latex Z$) on the polarization states of a single photon to confirm Ozawa’s result, and to experimentally violate the MDR. \u00a0The experiment is very cool, since it crucially relies on entanglement induced between the probe photon and the measurement apparatus.
\nThe bottom line: the uncertainty principle emerges completely unscathed, but the original hand-wavy MDR succumbs to both theoretical and now experimental violations.
\nNow let’s look at the BBC article. Right from the title and the subtitle, they get it wrong. “Heisenberg uncertainty principle stressed in new test”—no, that’s wrong—“Pioneering experiments have cast doubt on a founding idea…”—also no—the results were consistent with the HUP, and actually corroborated Ozawa’s theory of measurement–disturbance! Then they go on to say that this “could play havoc with ‘uncrackable codes’ of quantum cryptography.” The rest of the article has a few more whoppers, but also\u00a0some mildly redeeming features; after such a\u00a0horrible start<\/a>, though, you might as well quietly leave the pitch.\u00a0Please science journalists, try to do better next time.<\/p>\n","protected":false},"excerpt":{"rendered":"

Over at BBC News, there is an\u00a0article about a recently published\u00a0paper\u00a0(arXiv) by Lee Rozema et al. that could lead to some, ehm, uncertainty about the status of the Heisenberg Uncertainty Principle (HUP). Before\u00a0dissecting\u00a0the BBC article, let’s look at the paper by Rozema et al. The title is “Violation of Heisenberg\u2019s Measurement–Disturbance Relationship by Weak Measurements”.\u00a0While … <\/p>\n

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